14-02-2013, 03:23 PM
SOBEL EDGE DETECTION METHOD FOR MATLAB
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ABSTRACT
Sobel which is a popular edge detection method is considered in this work. There exists a
function, edge.m which is in the image toolbox. In the edge function, the Sobel method
uses the derivative approximation to find edges. Therefore, it returns edges at those points
where the gradient of the considered image is maximum. The horizontal and vertical gradient
matrices whose dimensions are 3×3 for the Sobel method has been generally used in the
edge detection operations. In this work, a function is developed to find edges using the
matrices whose dimensions are 5×5 in matlab.
INTRODUCTION
Edge detection is the process of localizing pixel intensity transitions. The edge detection
have been used by object recognition, target tracking, segmentation, and etc. Therefore, the
edge detection is one of the most important parts of image processing.
There mainly exists several edge detection methods (Sobel [1,2], Prewitt [3], Roberts [4],
Canny [5]). These methods have been proposed for detecting transitions in images. Early
methods determined the best gradient operator to detect sharp intensity variations [6].
Commonly used method for detecting edges is to apply derivative operators on images.
Derivative based approaches can be categorized into two groups, namely first and second
order derivative methods. First order derivative based techniques depend on computing the
gradient several directions and combining the result of each gradient. The value of the
gradient magnitude and orientation is estimated using two differentiation masks [7].
In this work, Sobel which is an edge detection method is considered. Because of the
simplicity and common uses, this method is prefered by the others methods in this work.
The Sobel edge detector uses two masks, one vertical and one horizontal. These masks
are generally used 3×3 matrices. Especially, the matrices which have 3×3 dimensions
are used in matlab (see, edge.m).
SOBEL EDGE DETECTION
Standard Sobel operators, for a 3×3 neighborhood, each simple central gradient
estimate is vector sum of a pair of orthogonal vectors [1]. Each orthogonal vector is a
directional derivative estimate multiplied by a unit vector specifying the derivative’s direction.
The vector sum of these simple gradient estimates amounts to a vector sum of the 8
directional derivative vectors.
EDGE DETECTION FUNCTION
Each direction of Sobel masks is applied to an image, then two new images are
created. One image shows the vertical response and the other shows the horizontal
response. Two images combined into a single image. The purpose is to determine the
existence and location of edges in a picture.
This two image combination is explained that the square of created masks pixel
estimate coincidence each other as coordinate are summed. Thus new image on which
edge pixels are located obtained the value which is the squared of the above summation.
The value of threshold in this above process is used to detect edge pixels [10].
An algorithm is developed to find edges using the new matrices and then, a matlab
function, which is called as Sobel5×5.m, is implemented in matlab. This matlab function
requries a grayscale intensity image, two-dimensional array. The result which is returned by
this function is the final image in which the egde pixels are denoted by white color (see,
Appendix).
CONCLUSION
Sobel edge detection method is considered in this work. The common Sobel edge
detector which have 3×3 horizontal and vertical masks is used in the edge function, in the
image toolbox of matlab. These masks are extend to 5×5 dimension masks. A matlab
function, called as Sobel5×5 is developed. This function and the edge function are analyse
the image set. The results are given in Appendix section.